Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena. The advantages of abstraction in mathematics are: It reveals deep connections between different areas of mathematics, Known results in one area can suggest conjectures in a related area, Techniques and methods from one area can be applied to prove results in a related area, The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and require a degree of mathematical maturity and experience before they can be assimilated.

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On Redemption

To redeem the past and to transform every ‘It was’ into an ‘I willed it thus!’ – that alone I call redemption!

Nietzsche, "Thus Spoke Zarathustra"

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Andrei Tarkovsky

“We can express our feelings regarding the world around us either by poetic or by descriptive means... I prefer to express myself metaphorically. Let me stress: metaphorically, not symbolically. A symbol contains within itself a definite meaning, certain intellectual formula, while metaphor is an image. An image possessing the same distinguishing features as the world it represents. An image — as opposed to a symbol — is indefinite in meaning. One cannot speak of the infinite world by applying tools that are definite and finite. We can analyse the formula that constitutes a symbol, while metaphor is a being-within-itself, it’s a monomial. It falls apart at any attempt of touching it."